displacement response to axial cycling of piles driven in sand

The effects of cycling on axial capacity are interpreted by reference to stable, metastable or unstable zones defined in a normalised cyclic stability interaction diagram.. Notation a pe

Displacement response to axial

cycling of piles driven in sand

Siya P RimoyMSc, DIC

PhD research student in geotechnics, Department of Civil and

Environmental Engineering, Imperial College London, London, UK

Richard J JardineFREng, FICE, FCGI

Professor in Geomechanics, Dean of Engineering, Department of Civil and

Environmental Engineering, Imperial College London, London, UK

Jamie R StandingMSc, PhD, DIC, MICE Senior Lecturer in Geotechnics, Department of Civil and Environmental Engineering, Imperial College London, London, UK

A review of the load applied to multi-pile offshore wind turbine foundations is presented, from which the need to consider the response to axial cyclic loading is emphasised The paucity of available data on field tests on driven piles in sand is noted A comprehensive data set of multiple axial cyclic and static tests conducted on seven industrial-scale steel pipe-piles at a marine sand site in Dunkerque, France, is re-examined in this paper The effects of cycling on axial capacity are interpreted by reference to stable, metastable or unstable zones defined in a normalised cyclic stability interaction diagram A detailed analysis is made of the load–displacement and stiffness response associated with each mode of cycling It is shown that in all cases the piles’ cyclic stiffnesses show only minor changes until cyclic failure is approached The patterns of permanent cyclic strain accumulation are sensitive to the applied mean and cyclic loading levels Whereas displacements accumulate rapidly over just a few cycles in the unstable zone, extended cycling in the stable zone leads to minimal accumulated displacements and constant transient cyclic displacements

Notation

a permanent accumulated cyclic displacement

D pile external diameter

d transient cyclic displacement

Gcompression shear stiffness in triaxial compression

Gextension shear stiffness in triaxial extension

Gs specific gravity

ID density index

K0 coefficient of earth pressure at rest

kl load–displacement axial cyclic stiffness during

loading

kN¼1 load–displacement axial cyclic stiffness at first

cycle

kRef initial maximum reference load–displacement

secant stiffness

ku load–displacement axial cyclic stiffness during

unloading

L pile embedded length

Nf number of cycles to failure in pile axial cyclic

loading

Qmax maximum axial cyclic load

Qmean mean axial cyclic load

Qmin minimum axial cyclic load

QRef first axial load step applied

QT pile tension capacity

qc CPT tip resistance

Rcla mean centreline roughness

S stable axial cyclic loading condition

T shear force applied to pile shaft

t pipe-pile wall thickness

z local settlement inducing shear force T

ªsat saturated bulk unit weight

˜Q pile-head axial load increment

˜s pile-head settlement or uplift displacement

increment

9cv angle of constant-volume interface shearing

resistance

9p angle of peak interface shearing resistance

s shear strain invariant

 9n effective normal stress

9cs angle of critical state shearing resistance

9p angle of peak shearing resistance

The axial cyclic response of driven-pile foundations can be important in the design of conventional offshore oil and gas platforms and onshore facilities such as towers and pylons (Jardine, 1991; Poulos, 1988) It may be still more critical in offshore wind turbines that rely on tripods or jacket structures Turbines commissioned in relatively shallow waters (, 30 m) are currently mostly founded on monopiles (75%) or gravity-based structures (20%) (Gavin et al., 2011), whose axial response is often not a significant concern With deeper water sites, jacket and tripod structures founded on open-ended driven pipe-piles become more attractive (e.g Seidel, 2007) The lateral and moment loads imposed by wind or wave action can be large in

comparison with self-weights, leading to multiple modes of axial

and lateral cyclic loading acting on the foundation piles While

lateral loading model test data have been reported for monopiles

(Leblanc et al., 2010), less guidance is available regarding

full-scale displacement accumulation and stiffness responses under

axial cycling

Jardine et al (2012) reviewed the potential effects of cyclic

loading on offshore piles, and considered how these may be

addressed in practical design They outlined the indicative ranges

for cyclic loading components that might apply to the range of

multiple pile structures listed in Table 1, noting that the loads vary

with platform weight, water depth, metocean environment, and

structural form In these examples the worst storm events

(100-year return period for oil/gas and 50-(100-year return period for wind

energy) set the design-critical conditions Following the cyclic

loading convention in Figure 1, the average ratio of Qcyclic/Qmean

on the windward side is around 7.8, and that on the leeward is just

above 1.0, the limiting value for the pile loads to become tensile

The maximum compressive loads developed on the leeward side,

Qmax¼ Qmean+ Qcyclic, usually constitute the critical conventional

design case, although this may alter after accounting for cyclic

loading effects Cyclic effects may be more marked for the tensile

load cases, but there are broad spreads of ratios between both wind

turbines and conventional oil and gas jackets For example, tension

is more critical for Case G, of a tripod wind turbine founded in sand, and it could also be with some wind turbine jacket structures

in deeper water

Jardine et al (2012) summarised data from field investigations involving the response to axial cyclic loading of steel piles; they noted 14 case histories in clay and only one in silica sands at Dunkerque, France, reported by Jardine and Standing (2000, 2012) As described by Merritt et al (2012), cyclic pile behaviour under the first few hundred cycles represents the most critical condition to be satisfied in design, and the Jardine and Standing (2000) tests represent the only field study of which the current authors are aware that investigates such behaviour up to 1000 cy-cles More extended tests on sands have been performed in laboratory centrifuges (Puech et al., 2012) and calibration chambers (Tsuha et al., 2012), and are planned for a secondary campaign of full-scale tests at Dunkerque (Puech et al., 2012)

A range of analytical techniques that can be applied in axial cyclic design were set out by Jardine et al (2012), and Merritt et

al (2012) described a practical application to a wind farm founded in sand Both papers emphasise the use of interactive cyclic stability diagrams to guide the assessment of global axial cyclic load capacity degradation for driven piles, as advocated previously by Karlsrud et al (1986), Poulos (1988) and Jardine and Standing (2000) These cyclic stability diagrams consider the interaction effects of cyclic and mean loads (normalised by static capacity before cycling) and the number of cycles applied Such interaction diagrams may be zoned to identify a cyclically stable (S) region where there is no reduction of load capacity after N cycles, a metastable (MS) area where some reduction of load capacity occurs after N cycles, and an unstable (US) zone where cyclic failure develops within a small specified number of cycles Tsuha et al (2012) proposed quantitative definitions for the three zones when reporting model pile tests in silica sand They also provided insights into the interface shear behaviour and sand mass response to cyclic pile loading Jardine and Standing (2012) applied a similar scheme in interpretation of their field tests at Dunkerque (Figure 2) Stable cyclic responses were associated

Jacket code, location and type Water depth: m Leeward Qcyc/Qmean Windward Qcyc/Qmean

Table 1.Indicative ranges for cyclic loading components; sites A

to F predominantly clay, site G mainly sand (after Jardine et al.,

2012)

cyclic max min mean max min

Qmax

Qmin

Q

Qcyclic

Qmean Cyclic period, T

Figure 1.Load–controlled axial cycling illustrated (Tsuha et al.,

2012)

with low and stabilising accumulated displacements up to a

relatively large number of cycles ( 1000), but behaviour was

deemed unstable if large displacements accrued leading to cyclic

failure within less than 100 cycles The intermediate metastable

response zone was characterised as showing permanent

displace-ment trends that did not stabilise between 100 and 1000 cycles

and resulted in either failure or degradation in axial capacity

A first-stage screening process for axial cyclic design is described

in Figure 3 by plotting on the Dunkerque cyclic interaction

diagram (Jardine and Standing, 2012) the most critically loaded

piles from the range of storm conditions on the platforms listed

in Table 1 In this simplified treatment it is assumed that all the

piles were designed to give working stress design (WSD) factors

of safety (FoS) of 1.5 with respect to their most critical single

ultimate limit state (ULS) storm load; higher factors were in fact

adopted in several of the practical cases considered For example,

referring to case A in Table 1 and Figure 3, for Qmax=QT¼

(Qmeanþ Qcyc)=QT¼ 1=1:5 and Qcyc/Qmean¼ 0.36, Qmean/QT¼

0.49 and Qcyc/QT¼ 0.18 Jardine et al (2012) noted that leeward

compressive conditions dominated in cases A to F, whereas

tension was more critical in case G Pile-end resistance and group

action are not considered in this illustration, but should be

addressed in practice The illustrative cases shown in Figure 3

have ULS events that plot above the stable contour, so some

damage could be expected for each installation if founded in

deposits comparable to the Dunkerque medium-dense marine

sand Cases B, D, E, F and G show a progression of reducing

proximity to the Nf ¼ 1000 contour, and hence increasing

potential of cycling loading degradation Case C plots above the

Nf¼ 100 contour, indicating a considerable potential impact on

this structure’s foundation performance Cyclic loading can

reduce the safety factor very significantly below 1.5 based on static shear strength, but by degrees that differ in each of the cases considered

This paper focuses on further interpretation of the axial cycling experiments by Jardine and Standing (2000, 2012) at Dunkerque

It reviews the multiple cyclic loading tests performed that were interspersed with reference static tension capacity tests The stiffness responses and cyclic displacements associated with each mode of cycling are examined, referring to the site-specific normalised cyclic interaction stability diagram

Seven full-scale open-ended steel pipe-piles were installed as part

of the GOPAL project (Parker et al., 1999) They were 457 mm in diameter, with 13.5 mm wall thickness (increased to 20 mm over the top 2.5 m); six had embedded lengths around 19 m, and one was driven to 10 m The piles were driven in the flat area close to Dunkerque Port Ouest Industrial Zone, where an earlier CLAROM driven-pile test programme had been conducted (Brucy et al., 1991) The site offers a relatively deep profile of dense Flandrian marine sands, similar to those at multiple North Sea offshore oil and gas platforms founded on open-ended driven steel pipe-piles (Thomas, 1990) and locations where wind turbine arrays are planned (e.g Merritt et al., 2012) Six of the test piles (R1–R6) had been installed to provide reaction for the GOPAL project test piles C1 and JP1 The reaction loading applied either one or two significant tension load cycles to R1–R6 prior to the cyclic loading study, with maxima , 60% of the piles’ ICP-05 design capacities (Jardine et al., 2005a) The piles’ cyclic capacity trends

1

1·0 0·8

0·6 0·4

0·2 0

Qmean/QT

QQcyclic

0·2

0·4

0·6

0·8

1·0

Set 2

Set 3 3 206 24

1

12

41

9 27 345

⬎221

⬎200

No cyclic failure First failure Cyclic failure after previous cyclic

or static failure

⬎1000

S ⫽ stable cycle zone

MS metastable cycle zone

US ⫽ unstable cycle zone

⫽ US

MS

S

Set 1

Figure 2.Axial cyclic interaction diagram for full-scale pile tests in

Dunkerque silica marine sands (Jardine and Standing, 2012)

QQcyclic

1·0 0·8

0·6 0·4

0·2

Qmean/QT

N

f 100

⫽

Nf

1000

⫽

0 0 0·2 0·4 0·6 0·8

1·0

A – Oil and gas

B – Oil and g as

C – Oil and g as

D – Oil and g as

E – Wind turbine

F – Wind turbine

G – Wind turbine WSD FoS ⫽ 1·5 Unstable

Metastable

Stable

Figure 3.Illustration of potential cyclic effects for WSD FoS ¼ 1.5 design conditions compared with Dunkerque contours of stable, metastable and unstable condition in normalised cyclic interaction diagram

have been reported by Jardine and Standing (2000, 2012), and

Jardine et al (2006) reported the piles’ remarkable static tension

capacity–time trends Chow (1997) reported static and cyclic tests

at the same site with the ICP (Imperial College pile) pile, which

carries pore pressure sensors The pore pressures showed a fully

drained response Although this is also expected at field scale with

large piles in clean sands, partially drained behaviour might apply

in lower-permeability deposits, as may be checked by inspecting

piezocone data and applying consolidation analyses

Jardine et al (2006) and Jardine and Standing (2012) detailed the

test piles’ layout plan (Figure 4), pile tension testing set-up

(Figure 5), and geotechnical profiling, which included multiple

cone penetrometer test (CPT), DMT and seismic soundings as

well as extensive laboratory tests on samples from a 26 m deep

borehole The site profile (Figure 6) consists of 3 m of hydraulic

marine sand fill overlying an extensive depth of Flandrian marine

sand deposited over three local transgressions between 2100 and

900 years BP (Somme´, 1969) The Dunkerque profile includes an

organic layer between 7.6 m and 8.2 m, associated with sea-level

transgressions, and two further, deeper organic bands The CPT

qc tip resistances vary with depth between 10 and 35 MPa,

averaging around 21 MPa over the 19 m pile lengths The

ground-water table was reported at 4 m, showing no tidal variations The

sands’ particle size distributions (PSD) are shown in Figure 7, and other index properties are given in Table 2 Summary observations are given in Table 3 regarding the site-specific laboratory characterisation reported by Chow (1997), supplemen-ted by extensive advanced laboratory testing by Kuwano (1999) Jardine et al (2005b) showed that the piles’ static load–displace-ment characteristics can be reproduced with reasonable accuracy

by non-linear finite-element analyses based on

(a) the non-linear laboratory stiffness data (b) local shaft stress distributions assessed through the ICP procedures (incorporating allowance for pile–soil interface slip, as described by Jardine et al., 2005a)

(c) allowance for the pile ageing behaviour

Any application of the cyclic pile test results should consider how they may scale to the problem in hand The key points to consider are the pile slenderness ratio L/D, and the effective axial stiffness of the piles compared with the shear stiffness of the soil mass The pile stiffness depends on the steel modulus, the pile wall thickness (t ) and outside diameter Pile C1 had an L/D 22, whereas R1 to R6 had L/D 42 The latter L/D value is typical

of many offshore jacket piles, but lower values are typical for monopiles and possibly for multi-pile wind turbine structures All the test piles had D/t ratios of 33.8 over most of their embedded lengths, which may be typical of jacket structures, but are low for wind turbine installations (Jardine, 2008; Merritt et al., 2012) The Dunkerque conditions may be typical for southern North Sea sites, but greater stiffness can be expected at denser sand sites, where qcvalues exceed 50 MPa

In cases where the pile make-up and soil stiffness characteristics are clearly different, the global cyclic stability diagrams can be reformulated to consider local cyclic degradation processes through a cyclic T–z approach, as summarised for example by Puech et al (2012) and applied to the Dunkerque case by Atkins Consultants Ltd (2000) using an approach such as that outlined in the ICP design procedures (Jardine et al., 2005a), and detailed in Jardine and Standing (2012)

The cyclic testing programme performed is detailed in Table 4 Note that only static tests were performed on pile R1 Pile-head loads were controlled by an automated hydraulic system and beam arrangement supplied by Precision Measurement and Con-trol (PMC) Ltd of Teesside UK (Jardine et al., 2006) The loads applied were measured through a high-quality load cell, and displacements were monitored by four LVDTs fixed to reference beams supported by steel poles driven at least 3 m away from the reaction system (Figure 5) The axial cyclic loading was con-trolled by a regulator that imposed near-sinusoidal waves with maxima and minima that could be controlled to within 5 kN over long-duration tests The cyclic rates ranged between 1 and

2 min per cycle, depending on the pile response

N

A

CPT R2-3 JP1 CPT R5-6

CPT GP1.B

A

Insitut

Pasteur

C1

Figure 4.Plan showing layout of test and reaction piles and CPTs

from GOPAL project in Dunkerque, France (after Jardine and

Standing, 2012)

The test code sequence given in Table 4 refers to the testing

phase (of which there were three), the pile identifier (e.g R2),

and then the test type (CY¼ cyclic, T ¼ static tension) and

number of tests for the respective pile No cycling was conducted

in phase 1 The cyclic programme was organised into two

campaigns: phase 2, October–November 1998; and phase 3, April

1999 The load-controlled tests involving only tensile pile-head

loads are termed ‘one-way’, and tests where cycles ranged from tension to compression are referred to as ‘two-way’; tension loads and upward displacement responses are taken as positive through-out Definitions relating to cyclic loading are shown in Figure 1 Reference static tension tests to failure (T) were conducted after most of the cyclic tests These were performed to assess the effects of the applied axial cyclic loading on the operational static

500 t hydraulic jack and load cell

914 419 5·3 m long -beam

⫻

L

400 mm

400 mm

914 mm

914 mm

200 mm

500 mm

Displacement and reference system

6 m 1 m ground panel

⫻

Levelled sand

6 m (a)

Tension

Load-spreading beams

914 419 5·3 m long -beam

⫻

L

Displacement and reference system

6 m (b)

PMC tension head

6 m

Figure 5.Details of test rig (not to scale) (after Jardine et al.,

2006): (a) elevation; (b) plan

tension (shaft) capacity The static tests similarly served to isolate any effects of previous (static or cyclic) loading phases from the current axial cyclic behaviour Table 5 summarises the load test capacities

6.1 Cyclic failure criteria

Following Tsuha et al (2012) and Jardine and Standing (2012), the axial cycling displacement responses are classified as stable, metastable or unstable, applying the following criteria

(a) Stable (S): Low and stabilising accumulated axial displacements that remain below 0.01D and show slow rates

of change (< 1 mm/1000 cycles) up to N > 1000 without causing any loss of operational static shaft capacity

0

2

4

6

8

10

12

14

16

18

20

22

24

Borehole log 0 10 CPT20qc: MPa30 40 0 100 200CPT : kPafc300 400

Very dense, light brown, uniform, fine to medium, subrounded sand with occasional shell fragments (hydraulic fill)

GWL Dense with shell fragments (Flandrian sand)

Organic layer Dense, green-brown and grey-brown, uniform fine to medium, subrounded sand with some shell fragments

(Flandrian sand)

Becoming very dense

Figure 6.Typical site profile for CLAROM/ Imperial College test

site (Jardine et al., 2006)

10 1

0·1 0·010

10

20

30

40

50

60

70

80

90

Gravel Sand

Particle size: mm Silt

Figure 7.Particle size distributions envelope of Dunkerque sand

(after Jardine and Standing, 2000)

Specific gravity, Gs SiO2: % Feldspar: % CaCO3: % Averageªsat: kN/m3 Average ID: %

Table 2.Index properties of Dunkerque sand

(b) Metastable (MS): Axial displacements accumulate

(0.01D , accumulated displacements < 0.1D) at moderate

rates (1 mm/1000 cycles , rates < 1 mm/10 cycles),

potentially leading to some degradation of the operational

static shaft capacity, but not causing failure within 100 cycles

(c) Unstable (US): Cyclic failure within 100 cycles, involving

either accumulated permanent cyclic displacements 0.1D

or rates of accumulation of permanent cyclic displacements

that increase to 1 mm/10 cycles Shaft capacity degradation

is potentially very significant

The cyclic tests are reported and analysed with reference to the cyclic stability interaction diagram shown in Figure 2 from Jardine and Standing (2012) The static tension capacities varied with time and cyclic loading history The reference QT values employed in Figure 2 are those applying at the time of testing

K0consolidated undrained (CK0U) triaxial stress path tests (K0¼ 0.35), ID¼ ,75% Compression9p¼ 378 Kuwano

(1999) Extension9p¼ 358

Critical state9cs¼ 328

K0consolidated undrained (CK0U) triaxial stress path tests (K0¼ 0.35), shear modulus at

s¼ 0.005%, ID¼ ,75%

Gcompression¼ 111 MPa Kuwano

(1999)

Gextension¼ 230 MPa

(1999)

9p¼ 39.48 Sand–mild steel interface (Rcla¼ 9.8m) direct shear test 9p¼ 30.88

9cv¼ 26.88 Aged sand–stainless steel interface (Rcla¼ 9.8m) direct shear tests, 63 days’ ageing 9p¼ 31.08 Chow (1997)

9cv¼ 27.58

No change of either 9 cv or 9 p with ageing Creep densification, increased shear stiffness and stronger dilation with ageing supposedly from microstructural rearrangement of the sand grains and their contacts.

Table 3.Mechanical properties of Dunkerque sand

Test mode Test code Qcyclic: kN Qmean: kN QT: kN Nf

Test code explained (XX M.YY.ZZN):

XX ¼ pile response mode (S, stable; MS, metastable; US, unstable)

M ¼ testing campaign phase (out of 3)

YY ¼ pile name (C1, R1–R6)

ZZ ¼ test type (T, static tension; C, static compression; CY, axial cyclic)

N ¼ test number on pile in sequence from installation.

Table 4.Axial cyclic loading testing programme (from Jardine and

Standing, 2000)

The ranges of cyclic loading conditions (Qmean, Qcyclic) considered

are normalised by the current reference static capacity, QT:The

diagonal line (Qmean/QT, Qcyclic/QT) (1, 0) to (0, 1) forms the

upper static limit (N¼ 1) Rate effects in shaft capacity are likely

to be small in sands, and the pile-loading cases are mapped into

cyclic stability zones, which are assigned to conform broadly to

the number of cycles required to induce cyclic failure under the

specified conditions The cyclic loading experienced in service by

offshore driven piles may involve millions of low-level cycles,

while severe storms are likely to impose a relatively small

number of severe load cycles Recovery of capacity degradation

can take place between severe storms (Jardine and Standing,

2000)

The 14 load-controlled axial cyclic tests gave a range of

outcomes, with one stable loading (set 1), four metastable

loading (set 2) and nine unstable loading (set 3) responses

indicated in Figure 2 In analysing the cyclic loading data,

displacements have been assessed in two ways The permanent

accumulated cyclic displacement, shown as a in Figure 8, is

cumulative, usually increasing with the number of cycles It is

measured with respect to the Qmax point of the first cycle (see

Figures 1 and 8) The second measure of displacement, d, is the

transient cyclic displacement that occurs for each cycle, and

which may increase with cycling, especially under metastable

and unstable loading conditions Analyses of how the piles’

axial cyclic stiffness (defined in Figure 8) responses, permanent accumulated cyclic displacements and the transient cyclic dis-placements evolved with number of cycles during cyclic loading are now presented

Test code Tension capacity: kN Comment

2.R3.T1 2000* No failure on loading to 10.3 mm displacement

2.R3.T4 ,1655 ‘Stick–slip’ failure in ‘quick’ test

2.R4.T1 2000* No failure on loading to 8.7 mm displacement

2.R4.T5 ,2000 Brittle ‘stick–slip’ failure, reducing to ,1450 kN

3.R4.T7 ,2490 Brittle ‘stick–slip’ failure (reducing to ,1900 kN) in ‘quick’ test

2.R5.T1 2000* With 8.9 mm displacement; estimated capacity 2450 kN

2.R5.T4 ,1300 ‘Stick–slip’ failure in ‘quick’ test

3.R5.T5 ,1795 Brittle failure reducing to 1636 kN

2.R6.T1 2400 With 30 mm displacement; estimated capacity 2450 kN

2.R6.T5 ,1325 ‘Stick–slip’ failure in ‘quick’ test

2.C1.C1 2820 After 34 mm, load at 46 mm estimated at 2850 kN

* Tests curtailed at maximum initial rig capacity of 2000 kN.

Table 5.Reference static tension capacities (from Jardine and

Standing, 2000)

2 1

N⫽ 0

Qmax

kl

a d k k

: Permanent : Transient cyclic displacement : Unloading cyclic stiffness : Loading cyclic stiffness

accumulated cyclic displacement

u l

ku

d

a

Displacement: mm

Qmin

Figure 8.Illustration of stiffness and displacement parameters used in analyses

6.2 Pile axial cyclic stiffness

Figure 9 plots load–displacement results from slow,

maintained-load, first-time tension tests for seven of the piles driven at

Dunkerque (i.e tests 2.C1.T2, 1.R1.T1, 3.R2.T1, 2.R3.T1,

2.R4.T1, 2.R5.T1 and 2.R6.T1 from Table 5) The initial

maxi-mum reference secant stiffness kRef¼˜Q/˜s is defined by

considering the first load step applied (defined as QRef), which

was 100 kN for C1 and 200 kN for R1 to R6 As noted by Jardine

et al (2005b), the piles’ load–displacement behaviour is highly

non-linear In Figure 10 the piles’ secant stiffness non-linearity,

assessed from the first-time tension loading tests shown in Figure

9, is represented by plotting the stiffnesses ratio, k/kRef, against

the ratio Q/QRef: Piles R2 to R6 (19 m long) show trends

common to but stiffer than the lower ultimate capacity 19 m long pile R1, which is stiffer than the shorter (10 m long) pile C1

The stiffness response under cycling is considered using the variables defined in Figure 8 Note that different cyclic stiffness values kl or ku may develop on the loading and unloading paths

of cyclic loading respectively The loading cyclic stiffness values,

kl, are considered first in relation to the reference stiffness kRef,

as shown in Figure 11(a) (stable and metastable tests) and Figure 12(a) (unstable tests) to examine the evolution of the piles’ stiffness under axial cycling Figures 11(b) and 12(b) show the same data, but with the kl values normalised by the loading

3500

3000

2500

2000

1500

1000

500

0

Pile-head displacement: mm

R1 R2 R3*

R4*

R5*

R6

Figure 9.Load–displacement curves for first-time monotonic

tension load tests *Tests curtailed at maximum initial rig capacity

20 15

10 5

0

0·2

0·4

0·6

0·8

1·0

R1

C1

Q Q/ Ref

R2–R6

Figure 10.Stiffness degradation of piles assessed from the

first-time axial static monotonic tension loadings normalised by the

reference stiffnesses plotted against load normalised by QRef

S 3.R4.CY6;Qcyc⫽ 0·2QT

MS 2.R3.CY2;Qcyc⫽ 0·3QT

MS 2.R4.CY2;Qcyc⫽ 0·34QT

MS 2.R5.CY2;Qcyc⫽ 0·3QT

MS 3.R6.CY6;Qcyc⫽ 0·42QT

kkl

1000 100

10

Qcyc⫽ 0·34QT

Qcyc⫽ 0·3QT

Qcyc⫽ 0·42QT

S 3.R4.CY6;Qcyc⫽ 0·2QT

MS 2.R3.CY2;Qcyc⫽ 0·3QT

MS 2.R4.CY2;Qcyc⫽ 0·34QT

MS 2.R5.CY2;Qcyc⫽ 0·3QT

MS 3.R6.CY6;Qcyc⫽ 0·42QT

kkl1

/N

1000 100

10 1

Cycles, N

(b)

1 0·2 0·4 0·6 0·8 1·0

All other metastable tests

Stable test

Cycles, N

(a)

Data not logged for the first 34 cycles

0 0·2 0·4 0·6 0·8 1·0 1·2

All other metastable tests

Stable test

Data not logged for the first 34 cycles

Figure 11.Axial cyclic loading stiffness (kl) responses normalised

in terms of (a) kRefand (b) kN¼1, plotted against number of cycles for stable and metastable loading tests

stiffness measured over the first loading cycle of each particular

test, kN¼1:

Figure 11(a) shows the results from the stable and metastable

axial cycling tests (sets 1 and 2 in Figure 2), with the Qcyclicvalue

for each test marked in the legend For the metastable loading

tests, the initial normalised stiffness values (i.e kl/kRef at N¼ 1)

clearly reduce as Qcyclic increases, as expected given the piles’

non-linear static response (the greater the proportion of QT

applied in the cycle, the smaller the initial secant stiffness) The two tests where cycling is applied at 0.3QT (MS 2.R3.CY2 and

MS 2.R5.CY2) follow roughly the same path, except that there is some scatter in the early data of the latter test The initial normalised stiffness for the stable loading test where the cycling

is applied at 0.2QT(S 3.R4.CY6) is in fact slightly lower than the value for the Qcyclic¼ 0.3QT tests It can be seen that continued cycling leads to only a marginal stiffness decrease (12%) over

1000 cycles in this stable loading 3.R4.CY6 test, with stiffness values stabilising, or even marginally increasing, after 200 cycles Compared with this stable test, the unfailed metastable loading tests 2.R3.CY2 and 2.R4.CY2 showed marginally more pro-nounced final stiffness degradations (of about 16%) up to the end

of cycling The failed metastable loading tests 2.R5.CY2 and 3.R6.CY6 showed similar trends over most of the cycling dura-tion, until sharp stiffness degradation set in as the piles ap-proached cyclic failure under the conditions given in Table 4 Similar trends are seen for the stiffness data normalised by kN¼1,

as shown in Figure 11(b)

The loading stiffness (kl) degradation trends for the unstable tests (Set 3 in Figure 2) are shown in Figures 12(a) and 12(b) By definition, all of these tests underwent cyclic failure and sudden stiffness degradation before reaching 100 cycles However, those piles that survived for longer than a few cycles retained their initial stiffness values until within a few cycles of final failure Slight variations are seen in the sharpness of the onsets to failure under similar cyclic loading levels, perhaps as a result of the complex testing sequences Stiffness degradation can be seen more clearly in Figure 12(b), where the loading stiffness klvalues are normalised by the initial cyclic stiffness kN¼1:

Seemingly anomalous stiffness behaviour is observed towards failure in the metastable and unstable loading tests when stiff-nesses are defined from the unloading cycle phases (ku), as seen in Figure 13 Whereas the C1 pile that was subjected to two-way loading cycles exhibited the same trends in stiffness degradation for both kland kuvalues, several of the piles subjected to one-way loading showed a typical initial gradual decrease of normalised stiffness (ku/kN¼1), but then exhibited apparently increasing ku values as cyclic failure was approached This reversal in normal-ised stiffness results from an increased opening-up of the load– unload hysteresis loops as cyclic failure approaches, with higher plastic displacements accumulating on the loading loop, and behaviour becoming increasingly dependent on cycle number These features lead to the progressively decreasing secant loading stiffnesses and apparently stiffer behaviour on unloading as cyclic loading approaches failure

6.3 Permanent accumulated cyclic displacements

The permanent accumulated cyclic pile-head displacements for the stable and metastable loading tests are shown in Figure 14, and Figure 15 refers to the unstable loading tests Also shown in Figures 14 and 15 are reference lines relating to the rate of accumulated displacements – that is, 1 mm/100 cycles and 1 mm/

kkl

100 10

kkl1

/N

100 10

1

Cycles, N

(b)

1

0·2

0·4

0·6

0·8

1·0

Cycles, N

(a)

US 3.R2.CY2 (0·40) US 2.R6.CY2 (0·36)

US 2.R3.CY3 (0·46) US 2.R6.CY4 (0·36)

US 2.R4.CY4 (0·44) US 2.C1.CY3 (0·74)

US 2.R5.CY3 (0·35) US 2.C1.CY4 (0·72)

US 2.C1.CY5 (0·66)

All unstable tests

0

0·2

0·4

0·6

0·8

1·0

1·2

All unstable tests

US 3.R2.CY2 (0·40) US 2.R6.CY2 (0·36)

US 2.R3.CY3 (0·46) US 2.R6.CY4 (0·36)

US 2.R4.CY4 (0·44) US 2.C1.CY3 (0·74)

US 2.R5.CY3 (0·35) US 2.C1.CY4 (0·72)

US 2.C1.CY5 (0·66)

Figure 12.Axial cyclic loading stiffness (kl) responses normalised

in terms of (a) kRefand (b) kN¼1, plotted against number of cycles

for unstable loading tests